PHYSICS

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a 100kg street light is supported equally by two ropes. one rope pulls up and to the right 40 degrees above the horizontal; the other pulls up and to the left 40 degrees . what is the tension of the rope?

  • PHYSICS -

    M*g = 100kg * 9.8N./kg = 980 N. = Wt. of
    st. light.

    T1*Cos(180-40) + T2*Cos40 = -980*cos270.
    -0.766T1 + 0.766T2 = 0.
    0.766T2 = 0.766T1.
    T1 = T2.

    T1*sin(180-40) + T2*sin40 = -980*sin270.
    0.643T1 + 0.643T2 = 980.
    Replace T2 with T1:
    0.643T1 + 0.643T1 = 980.
    1.286T1 = 980.
    T1 = 762 N. = T2.

  • PHYSICS -

    Or T1 = T2.

    T1*sin(180-40) + T1*sin40 = -980*sin270.
    0.643T1 + 0.643T1 = 980.
    1.286T1 = 980.
    T1 = 762 N. = T2.

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